Two members of an anti-Assad group have been shot dead in Lebanon, raising fears the turmoil in Syria is spilling over the border.

Sheikh Ahmed Abdul Wahid, a Sunni Muslim cleric, and Muhammed Hussein Miraib, both members of the Lebanon-based March 14 political alliance, were shot by Lebanese soldiers on Sunday.

A security official said they were shot in their car as it sped through a Lebanese army checkpoint without stopping.

Residents of the northern region of Akkar blocked off roads and burned tyres to protest against the deaths.

The main coastal highway as well as roads in the capital of Beirut were also blocked by enraged residents.

Some troops pulled out of Akkar to prevent tensions from escalating.

Many Sunni Muslims in Lebanon's north sympathise with the Sunni-led uprising against president Bashar al-Assad and accuse the Lebanese army of taking orders from Damascus.

Syrian government troops occupied parts of Lebanon until 2005.

Khaled Daher, a member of parliament from the Future Movement party, which is part of the March 14 alliance, said the two men had been assassinated.

"If shots were fired at the tyres, we would say there was a mistake. But we consider this a direct targeting from the army," he told Reuters.

"Frankly, we do not want to see the army here because it works at the service of the Syrian regime."

Lebanon's army released a statement confirming the deaths, but did not give any information on who was responsible or what led up to the shootings.

"The leadership of the army expresses deep regret for the death of the two victims," the statement said.

"It will immediately form an investigative committee comprised of senior officers and military police under the relevant court."

Prime minister Najib Mikati tried to quell growing tensions.

"The government is determined to continue to shoulder its national responsibilities amid this critical period in Lebanon and the region, and it will take all measures necessary to preserve civil peace," he said in a statement.

Lebanon is a tiny country still recovering from its own 15-year civil war and has seen sporadic violence between its many sects since that conflict ended in 1990.

Beirut-based political commentator Rami Khouri said recent violence in Lebanon's northern port of Tripoli had been linked to events in Syria.

"You have tensions in the area going back years but this has been exacerbated by the situation in Syria ... Syria is not the primary factor, but it is related," he said.